air resistance and the time of flight !!!

[peacefulheart]

Air resistance would decrease all of the following except ( projectile problem)

A. R (range)

B. h (height)

C. v ( initial velocity )

D.t.

1. I have no problem with answer C.

2. But how does air resistance decrease the fight time t.

thanks a lot

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[Captain Sisko]

Air resistance would decrease all of the following except ( projectile problem)

A. R (range)

B. h (height)

C. v ( initial velocity )

D.t.

1. I have no problem with answer C.

2. But how does air resistance decrease the fight time t.

thanks a lot

It depends on the problem. If it's a ball being dropped from a height it would increase. If it starts off on level ground it would decrease. The reason is time of flight is a function of vertical velocity, which is nominally affected by gravity. In the case of air resistance it's also affected by aerodynamic drag as a coefficient to velocity squared. So what happens is the Max vertical height is reduced and time of flight goes down.

 

[LoLCareerGoals]

OP already defined the problem. It is projectile motion.
I am actually curious about this as well. I understand the above explanation that max height reaching component of the projectile motion flight would in fact be shorter because air drag would effectively create a bigger g and decelerate initial v_vert to zero faster. However, I would also expect the 2nd component of the flight to take longer since it is now falling against the air resistance and this is accelerating downward slower.

 

[cheesier]

First, you have to understand that drag is a function of v^2. Air resistance only opposes the horizontal component of velocity at the apex of a projectile's trajectory, because at the very top, there is no vertical component. What happens is, the horizontal component gets pretty much wiped out near the apex, and a projectile falls almost vertically if there is a lot of air resistance (as opposed to the symmetric path that projectiles in a vacuum take). So you can't assume that air resistance affects the path up the same way it affects the path down for a projectile, because the paths are different. Drag is a function of velocity squared, and when the object is initially launched, it has a velocity and therefore experiences a drag force right away. When the object start to fall from its apex, its horizontal velocity has diminished greatly since its initial launch, and its y velocity is zero, so its net velocity is almost zero as well, and therefore its drag force is much smaller and it falls almost as if it were in a vacuum. The result is, going up doesn't take the same amount of time as going down.

 

[peacefulheart]

First, you have to understand that drag is a function of v^2. Air resistance only opposes the horizontal component of velocity at the apex of a projectile's trajectory, because at the very top, there is no vertical component. What happens is, the horizontal component gets pretty much wiped out near the apex, and a projectile falls almost vertically if there is a lot of air resistance (as opposed to the symmetric path that projectiles in a vacuum take). So you can't assume that air resistance affects the path up the same way it affects the path down for a projectile, because the paths are different. Drag is a function of velocity squared, and when the object is initially launched, it has a velocity and therefore experiences a drag force right away. When the object start to fall from its apex, its horizontal velocity has diminished greatly since its initial launch, and its y velocity is zero, so its net velocity is almost zero as well, and therefore its drag force is much smaller and it falls almost as if it were in a vacuum. The result is, going up doesn't take the same amount of time as going down.

1. Thanks for the explanation. It makes a lot of sense.

2. The air resistance helps the object going up, thus decreasing the time going up while the air resistance delays the object going down, thus increasing the time going down.

3. The reason behind this is that the air resistance has a greater effect on a fast-moving object ( greater velocity). Since the initial vertical velocity becomes zero at the apex and initial horizontal velocity diminishes a lot because of air resistance ( although without air resistance, the magnitude of initial horizontal velocity is the same during the up and down path).

4. Therefore, the time for the object up is less than the time for the object down. Overall, the flight time is decreased.

 

[cheesier]

1. Thanks for the explanation. It makes a lot of sense.

2. The air resistance helps the object going up, thus decreasing the time going up while the air resistance delays the object going down, thus increasing the time going down.

3. The reason behind this is that the air resistance has a greater effect on a fast-moving object ( greater velocity). Since the initial vertical velocity becomes zero at the apex and initial horizontal velocity diminishes a lot because of air resistance ( although without air resistance, the magnitude of initial horizontal velocity is the same during the up and down path).

4. Therefore, the time for the object up is less than the time for the object down. Overall, the flight time is decreased.

I'm not sure which part of the flight takes longer, because at launch you have greater air resistance + greater velocity. For the second half of the flight you have less air resistance initially, but a lower velocity. I'm sure it wouldn't be too big of a deal to calculate though (probably beyond the scope of the mcat). All in all, the flight time is reduced.

 

[Captain Sisko]

OP already defined the problem. It is projectile motion.
I am actually curious about this as well. I understand the above explanation that max height reaching component of the projectile motion flight would in fact be shorter because air drag would effectively create a bigger g and decelerate initial v_vert to zero faster. However, I would also expect the 2nd component of the flight to take longer since it is now falling against the air resistance and this is accelerating downward slower.

Just to clear something up, it still does depend on the problem. A cannon being fired off a cliff is projectile motion, but has a different answer than what you all are assuming, depending on the initial vertical height.

Other than that, you are generally correct in that the way up is decelerated more than the way down because the velocity is higher on the way up. But if the vertical distance from the start to the apex is different from that from the vertex to the landing point, adding air resistance can either increase or decrease time of flight.